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A356759
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Bit-reverse the odd part of the dual Zeckendorf representation of n: a(n) = A022290(A057889(A003754(n+1))).
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1
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0, 1, 2, 3, 4, 5, 6, 7, 9, 8, 10, 11, 12, 15, 17, 13, 16, 14, 18, 19, 20, 25, 22, 28, 30, 21, 26, 29, 23, 27, 24, 31, 32, 33, 41, 46, 36, 43, 38, 49, 51, 34, 42, 37, 47, 50, 35, 44, 48, 39, 45, 40, 52, 53, 54, 67, 59, 75, 80, 56, 70, 77, 62, 72, 64, 83, 85, 55
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OFFSET
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0,3
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COMMENTS
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This sequence is a self-inverse permutation of the nonnegative integers, similar to A345201 and A356331.
The dual Zeckendorf (or lazy Fibonacci) representation expresses uniquely a number n as a sum of distinct positive Fibonacci numbers; these distinct Fibonacci numbers can be encoded in binary, and the corresponding binary encoding, A003754(n+1), cannot have two consecutive nonleading 0's.
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LINKS
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FORMULA
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a(a(n)) = n.
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EXAMPLE
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For n = 49:
- the dual Zeckendorf representation of 49 is "1111010",
- reversing its odd part ("111101"), we obtain "1011110",
- so a(49) = 39.
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PROG
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(PARI) See Links section.
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CROSSREFS
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KEYWORD
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AUTHOR
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STATUS
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approved
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